LMFDB - Embedded newform 294.6.e.z.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,6,Mod(67,294)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("294.67");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	294.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$47.1528430250$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	294.79
Dual form			294.6.e.z.67.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 - 3.46410i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(2.25126 - 3.89930i) q^{5} +36.0000 q^{6} -64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(q+(2.00000 - 3.46410i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(2.25126 - 3.89930i) q^{5} +36.0000 q^{6} -64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-9.00505 - 15.5972i) q^{10} +(58.0955 + 100.624i) q^{11} +(72.0000 - 124.708i) q^{12} +85.4773 q^{13} +40.5227 q^{15} +(-128.000 + 221.703i) q^{16} +(16.6331 + 28.8093i) q^{17} +(162.000 + 280.592i) q^{18} +(317.688 - 550.252i) q^{19} -72.0404 q^{20} +464.764 q^{22} +(-1363.71 + 2362.02i) q^{23} +(-288.000 - 498.831i) q^{24} +(1552.36 + 2688.77i) q^{25} +(170.955 - 296.102i) q^{26} -729.000 q^{27} +5860.48 q^{29} +(81.0455 - 140.375i) q^{30} +(139.568 + 241.739i) q^{31} +(512.000 + 886.810i) q^{32} +(-522.859 + 905.619i) q^{33} +133.065 q^{34} +1296.00 q^{36} +(-1519.25 + 2631.41i) q^{37} +(-1270.75 - 2201.01i) q^{38} +(384.648 + 666.229i) q^{39} +(-144.081 + 249.555i) q^{40} -819.415 q^{41} +11100.2 q^{43} +(929.527 - 1609.99i) q^{44} +(182.352 + 315.843i) q^{45} +(5454.85 + 9448.09i) q^{46} +(-3703.70 + 6415.00i) q^{47} -2304.00 q^{48} +12418.9 q^{50} +(-149.698 + 259.284i) q^{51} +(-683.818 - 1184.41i) q^{52} +(6849.40 + 11863.5i) q^{53} +(-1458.00 + 2525.33i) q^{54} +523.153 q^{55} +5718.39 q^{57} +(11721.0 - 20301.3i) q^{58} +(11187.8 + 19377.9i) q^{59} +(-324.182 - 561.499i) q^{60} +(-6346.04 + 10991.7i) q^{61} +1116.55 q^{62} +4096.00 q^{64} +(192.432 - 333.302i) q^{65} +(2091.44 + 3622.47i) q^{66} +(26151.7 + 45296.0i) q^{67} +(266.129 - 460.949i) q^{68} -24546.8 q^{69} +60230.2 q^{71} +(2592.00 - 4489.48i) q^{72} +(38479.2 + 66647.9i) q^{73} +(6076.98 + 10525.6i) q^{74} +(-13971.3 + 24199.0i) q^{75} -10166.0 q^{76} +3077.18 q^{78} +(16798.0 - 29095.0i) q^{79} +(576.323 + 998.221i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(-1638.83 + 2838.54i) q^{82} -60574.9 q^{83} +149.782 q^{85} +(22200.4 - 38452.3i) q^{86} +(26372.2 + 45677.9i) q^{87} +(-3718.11 - 6439.95i) q^{88} +(46095.1 - 79839.0i) q^{89} +1458.82 q^{90} +43638.8 q^{92} +(-1256.11 + 2175.65i) q^{93} +(14814.8 + 25660.0i) q^{94} +(-1430.40 - 2477.53i) q^{95} +(-4608.00 + 7981.29i) q^{96} -152287. q^{97} -9411.46 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{2} + 18 q^{3} - 32 q^{4} + 108 q^{5} + 144 q^{6} - 256 q^{8} - 162 q^{9}+O(q^{10}) $ 4 * q + 8 * q^2 + 18 * q^3 - 32 * q^4 + 108 * q^5 + 144 * q^6 - 256 * q^8 - 162 * q^9	\( 4 q + 8 q^{2} + 18 q^{3} - 32 q^{4} + 108 q^{5} + 144 q^{6} - 256 q^{8} - 162 q^{9} - 432 q^{10} - 124 q^{11} + 288 q^{12} - 1440 q^{13} + 1944 q^{15} - 512 q^{16} - 1260 q^{17} + 648 q^{18} + 360 q^{19} - 3456 q^{20} - 992 q^{22} - 6524 q^{23} - 1152 q^{24} - 4482 q^{25} - 2880 q^{26} - 2916 q^{27} + 14176 q^{29} + 3888 q^{30} + 5904 q^{31} + 2048 q^{32} + 1116 q^{33} - 10080 q^{34} + 5184 q^{36} + 6040 q^{37} - 1440 q^{38} - 6480 q^{39} - 6912 q^{40} + 34776 q^{41} - 1216 q^{43} - 1984 q^{44} + 8748 q^{45} + 26096 q^{46} - 30456 q^{47} - 9216 q^{48} - 35856 q^{50} + 11340 q^{51} + 11520 q^{52} - 3964 q^{53} - 5832 q^{54} - 48672 q^{55} + 6480 q^{57} + 28352 q^{58} + 40752 q^{59} - 15552 q^{60} - 1368 q^{61} + 47232 q^{62} + 16384 q^{64} - 82980 q^{65} - 4464 q^{66} + 16224 q^{67} - 20160 q^{68} - 117432 q^{69} - 6408 q^{71} + 10368 q^{72} + 23976 q^{73} - 24160 q^{74} + 40338 q^{75} - 11520 q^{76} - 51840 q^{78} + 82160 q^{79} + 27648 q^{80} - 13122 q^{81} + 69552 q^{82} - 347472 q^{83} - 267400 q^{85} - 2432 q^{86} + 63792 q^{87} + 7936 q^{88} + 200556 q^{89} + 69984 q^{90} + 208768 q^{92} - 53136 q^{93} + 121824 q^{94} + 25640 q^{95} - 18432 q^{96} - 503856 q^{97} + 20088 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 + 18 * q^3 - 32 * q^4 + 108 * q^5 + 144 * q^6 - 256 * q^8 - 162 * q^9 - 432 * q^10 - 124 * q^11 + 288 * q^12 - 1440 * q^13 + 1944 * q^15 - 512 * q^16 - 1260 * q^17 + 648 * q^18 + 360 * q^19 - 3456 * q^20 - 992 * q^22 - 6524 * q^23 - 1152 * q^24 - 4482 * q^25 - 2880 * q^26 - 2916 * q^27 + 14176 * q^29 + 3888 * q^30 + 5904 * q^31 + 2048 * q^32 + 1116 * q^33 - 10080 * q^34 + 5184 * q^36 + 6040 * q^37 - 1440 * q^38 - 6480 * q^39 - 6912 * q^40 + 34776 * q^41 - 1216 * q^43 - 1984 * q^44 + 8748 * q^45 + 26096 * q^46 - 30456 * q^47 - 9216 * q^48 - 35856 * q^50 + 11340 * q^51 + 11520 * q^52 - 3964 * q^53 - 5832 * q^54 - 48672 * q^55 + 6480 * q^57 + 28352 * q^58 + 40752 * q^59 - 15552 * q^60 - 1368 * q^61 + 47232 * q^62 + 16384 * q^64 - 82980 * q^65 - 4464 * q^66 + 16224 * q^67 - 20160 * q^68 - 117432 * q^69 - 6408 * q^71 + 10368 * q^72 + 23976 * q^73 - 24160 * q^74 + 40338 * q^75 - 11520 * q^76 - 51840 * q^78 + 82160 * q^79 + 27648 * q^80 - 13122 * q^81 + 69552 * q^82 - 347472 * q^83 - 267400 * q^85 - 2432 * q^86 + 63792 * q^87 + 7936 * q^88 + 200556 * q^89 + 69984 * q^90 + 208768 * q^92 - 53136 * q^93 + 121824 * q^94 + 25640 * q^95 - 18432 * q^96 - 503856 * q^97 + 20088 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.00000	−	3.46410i	0.353553	−	0.612372i
$2$	2.00000	−	3.46410i	0.353553	−	0.612372i
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$4$	−8.00000	−	13.8564i	−0.250000	−	0.433013i
$5$	2.25126	−	3.89930i	0.0402718	−	0.0697528i	−0.845187	−	0.534471i	$-0.820511\pi$
$5$	2.25126	−	3.89930i	0.0402718	−	0.0697528i	0.885459	+	0.464718i	$0.153844\pi$
$6$	36.0000			0.408248
$7$		0			0
$7$		0			0
$8$	−64.0000			−0.353553
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$	−9.00505	−	15.5972i	−0.0284765	−	0.0493227i
$11$	58.0955	+	100.624i	0.144764	+	0.250739i	0.929285	−	0.369364i	$-0.120424\pi$
$11$	58.0955	+	100.624i	0.144764	+	0.250739i	−0.784521	+	0.620102i	$0.787091\pi$
$12$	72.0000	−	124.708i	0.144338	−	0.250000i
$13$	85.4773			0.140279			0.0701394	−	0.997537i	$-0.477656\pi$
$13$	85.4773			0.140279			0.0701394	+	0.997537i	$0.477656\pi$
$14$		0			0
$15$	40.5227			0.0465019
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	16.6331	+	28.8093i	0.0139589	+	0.0241775i	0.872920	−	0.487863i	$-0.162223\pi$
$17$	16.6331	+	28.8093i	0.0139589	+	0.0241775i	−0.858962	+	0.512040i	$0.828890\pi$
$18$	162.000	+	280.592i	0.117851	+	0.204124i
$19$	317.688	−	550.252i	0.201891	−	0.349686i	−0.747247	−	0.664547i	$-0.768625\pi$
$19$	317.688	−	550.252i	0.201891	−	0.349686i	0.949138	+	0.314861i	$0.101958\pi$
$20$	−72.0404			−0.0402718
$21$		0			0
$22$	464.764			0.204727
$23$	−1363.71	+	2362.02i	−0.537531	+	0.931031i	0.461505	+	0.887138i	$0.347310\pi$
$23$	−1363.71	+	2362.02i	−0.537531	+	0.931031i	−0.999036	+	0.0438936i	$0.986024\pi$
$24$	−288.000	−	498.831i	−0.102062	−	0.176777i
$25$	1552.36	+	2688.77i	0.496756	+	0.860407i
$26$	170.955	−	296.102i	0.0495961	−	0.0859029i
$27$	−729.000			−0.192450
$28$		0			0
$29$	5860.48			1.29401			0.647006	−	0.762485i	$-0.276021\pi$
$29$	5860.48			1.29401			0.647006	+	0.762485i	$0.276021\pi$
$30$	81.0455	−	140.375i	0.0164409	−	0.0284765i
$31$	139.568	+	241.739i	0.0260845	+	0.0451796i	0.878773	−	0.477240i	$-0.158363\pi$
$31$	139.568	+	241.739i	0.0260845	+	0.0451796i	−0.852688	+	0.522420i	$0.825029\pi$
$32$	512.000	+	886.810i	0.0883883	+	0.153093i
$33$	−522.859	+	905.619i	−0.0835795	+	0.144764i
$34$	133.065			0.0197408
$35$		0			0
$36$	1296.00			0.166667
$37$	−1519.25	+	2631.41i	−0.182442	+	0.315998i	−0.942711	−	0.333609i	$-0.891733\pi$
$37$	−1519.25	+	2631.41i	−0.182442	+	0.315998i	0.760270	+	0.649607i	$0.225067\pi$
$38$	−1270.75	−	2201.01i	−0.142759	−	0.247265i
$39$	384.648	+	666.229i	0.0404950	+	0.0701394i
$40$	−144.081	+	249.555i	−0.0142382	+	0.0246613i
$41$	−819.415			−0.0761279			−0.0380640	−	0.999275i	$-0.512119\pi$
$41$	−819.415			−0.0761279			−0.0380640	+	0.999275i	$0.512119\pi$
$42$		0			0
$43$	11100.2			0.915504			0.457752	−	0.889080i	$-0.348655\pi$
$43$	11100.2			0.915504			0.457752	+	0.889080i	$0.348655\pi$
$44$	929.527	−	1609.99i	0.0723820	−	0.125369i
$45$	182.352	+	315.843i	0.0134239	+	0.0232509i
$46$	5454.85	+	9448.09i	0.380092	+	0.658338i
$47$	−3703.70	+	6415.00i	−0.244563	+	0.423596i	−0.962009	−	0.273019i	$-0.911978\pi$
$47$	−3703.70	+	6415.00i	−0.244563	+	0.423596i	0.717446	+	0.696615i	$0.245311\pi$
$48$	−2304.00			−0.144338
$49$		0			0
$50$	12418.9			0.702520
$51$	−149.698	+	259.284i	−0.00805916	+	0.0139589i
$52$	−683.818	−	1184.41i	−0.0350697	−	0.0607425i
$53$	6849.40	+	11863.5i	0.334937	+	0.580128i	0.983473	−	0.181057i	$-0.0579517\pi$
$53$	6849.40	+	11863.5i	0.334937	+	0.580128i	−0.648536	+	0.761184i	$0.724618\pi$
$54$	−1458.00	+	2525.33i	−0.0680414	+	0.117851i
$55$	523.153			0.0233196
$56$		0			0
$57$	5718.39			0.233124
$58$	11721.0	−	20301.3i	0.457502	−	0.792417i
$59$	11187.8	+	19377.9i	0.418424	+	0.724732i	0.995781	−	0.0917601i	$-0.0292493\pi$
$59$	11187.8	+	19377.9i	0.418424	+	0.724732i	−0.577357	+	0.816492i	$0.695916\pi$
$60$	−324.182	−	561.499i	−0.0116255	−	0.0201359i
$61$	−6346.04	+	10991.7i	−0.218363	+	0.378215i	−0.954308	−	0.298826i	$-0.903405\pi$
$61$	−6346.04	+	10991.7i	−0.218363	+	0.378215i	0.735945	+	0.677041i	$0.236738\pi$
$62$	1116.55			0.0368890
$63$		0			0
$64$	4096.00			0.125000
$65$	192.432	−	333.302i	0.00564928	−	0.00978485i
$66$	2091.44	+	3622.47i	0.0590996	+	0.102364i
$67$	26151.7	+	45296.0i	0.711725	+	1.23274i	0.964209	+	0.265143i	$0.0854193\pi$
$67$	26151.7	+	45296.0i	0.711725	+	1.23274i	−0.252484	+	0.967601i	$0.581247\pi$
$68$	266.129	−	460.949i	0.00697944	−	0.0120887i
$69$	−24546.8			−0.620687
$70$		0			0
$71$	60230.2			1.41798			0.708988	−	0.705221i	$-0.249152\pi$
$71$	60230.2			1.41798			0.708988	+	0.705221i	$0.249152\pi$
$72$	2592.00	−	4489.48i	0.0589256	−	0.102062i
$73$	38479.2	+	66647.9i	0.845121	+	1.46379i	0.885516	+	0.464608i	$0.153805\pi$
$73$	38479.2	+	66647.9i	0.845121	+	1.46379i	−0.0403954	+	0.999184i	$0.512862\pi$
$74$	6076.98	+	10525.6i	0.129006	+	0.223444i
$75$	−13971.3	+	24199.0i	−0.286802	+	0.496756i
$76$	−10166.0			−0.201891
$77$		0			0
$78$	3077.18			0.0572686
$79$	16798.0	−	29095.0i	0.302824	−	0.524506i	−0.673951	−	0.738776i	$-0.735404\pi$
$79$	16798.0	−	29095.0i	0.302824	−	0.524506i	0.976774	+	0.214270i	$0.0687374\pi$
$80$	576.323	+	998.221i	0.0100680	+	0.0174382i
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$	−1638.83	+	2838.54i	−0.0269153	+	0.0466187i
$83$	−60574.9			−0.965157			−0.482578	−	0.875853i	$-0.660300\pi$
$83$	−60574.9			−0.965157			−0.482578	+	0.875853i	$0.660300\pi$
$84$		0			0
$85$	149.782			0.00224860
$86$	22200.4	−	38452.3i	0.323680	−	0.560630i
$87$	26372.2	+	45677.9i	0.373549	+	0.647006i
$88$	−3718.11	−	6439.95i	−0.0511818	−	0.0886495i
$89$	46095.1	−	79839.0i	0.616850	−	1.06841i	−0.373207	−	0.927748i	$-0.621742\pi$
$89$	46095.1	−	79839.0i	0.616850	−	1.06841i	0.990057	−	0.140667i	$-0.0449247\pi$
$90$	1458.82			0.0189843
$91$		0			0
$92$	43638.8			0.537531
$93$	−1256.11	+	2175.65i	−0.0150599	+	0.0260845i
$94$	14814.8	+	25660.0i	0.172932	+	0.299528i
$95$	−1430.40	−	2477.53i	−0.0162610	−	0.0281650i
$96$	−4608.00	+	7981.29i	−0.0510310	+	0.0883883i
$97$	−152287.			−1.64336			−0.821680	−	0.569949i	$-0.806963\pi$
$97$	−152287.			−1.64336			−0.821680	+	0.569949i	$0.806963\pi$
$98$		0			0
$99$	−9411.46			−0.0965093
$100$	24837.8	−	43020.4i	0.248378	−	0.430204i
$101$	53822.1	+	93222.6i	0.524997	+	0.909322i	0.999576	+	0.0291091i	$0.00926701\pi$
$101$	53822.1	+	93222.6i	0.524997	+	0.909322i	−0.474579	+	0.880213i	$0.657400\pi$
$102$	598.791	+	1037.14i	0.00569869	+	0.00987041i
$103$	60319.6	−	104477.i	0.560229	−	0.970345i	−0.437247	−	0.899341i	$-0.644047\pi$
$103$	60319.6	−	104477.i	0.560229	−	0.970345i	0.997476	−	0.0710033i	$-0.0226201\pi$
$104$	−5470.55			−0.0495961
$105$		0			0
$106$	54795.2			0.473672
$107$	−43057.2	+	74577.2i	−0.363568	+	0.629719i	−0.988545	−	0.150924i	$-0.951775\pi$
$107$	−43057.2	+	74577.2i	−0.363568	+	0.629719i	0.624977	+	0.780643i	$0.285108\pi$
$108$	5832.00	+	10101.3i	0.0481125	+	0.0833333i
$109$	33069.6	+	57278.2i	0.266602	+	0.461767i	0.967982	−	0.251020i	$-0.0807659\pi$
$109$	33069.6	+	57278.2i	0.266602	+	0.461767i	−0.701380	+	0.712787i	$0.747433\pi$
$110$	1046.31	−	1812.25i	0.00824473	−	0.0142803i
$111$	−27346.4			−0.210665
$112$		0			0
$113$	131608.			0.969588			0.484794	−	0.874628i	$-0.338895\pi$
$113$	131608.			0.969588			0.484794	+	0.874628i	$0.338895\pi$
$114$	11436.8	−	19809.1i	0.0824217	−	0.142759i
$115$	6140.16	+	10635.1i	0.0432947	+	0.0749886i
$116$	−46883.9	−	81205.2i	−0.323503	−	0.560324i
$117$	−3461.83	+	5996.06i	−0.0233798	+	0.0404950i
$118$	89502.8			0.591741
$119$		0			0
$120$	−2593.45			−0.0164409
$121$	73775.3	−	127783.i	0.458087	−	0.793430i
$122$	25384.2	+	43966.7i	0.154406	+	0.267439i
$123$	−3687.37	−	6386.71i	−0.0219762	−	0.0380640i
$124$	2233.09	−	3867.83i	0.0130422	−	0.0225898i
$125$	28049.5			0.160565
$126$		0			0
$127$	14437.3			0.0794284			0.0397142	−	0.999211i	$-0.487355\pi$
$127$	14437.3			0.0794284			0.0397142	+	0.999211i	$0.487355\pi$
$128$	8192.00	−	14189.0i	0.0441942	−	0.0765466i
$129$	49951.0	+	86517.6i	0.264283	+	0.457752i
$130$	−769.727	−	1333.21i	−0.00399465	−	0.00691893i
$131$	159608.	−	276450.i	0.812600	−	1.40747i	−0.0984380	−	0.995143i	$-0.531385\pi$
$131$	159608.	−	276450.i	0.812600	−	1.40747i	0.911038	−	0.412322i	$-0.135282\pi$
$132$	16731.5			0.0835795
$133$		0			0
$134$	209213.			1.00653
$135$	−1641.17	+	2842.59i	−0.00775031	+	0.0134239i
$136$	−1064.52	−	1843.80i	−0.00493521	−	0.00854803i
$137$	25267.0	+	43763.7i	0.115014	+	0.199211i	0.917785	−	0.397077i	$-0.129975\pi$
$137$	25267.0	+	43763.7i	0.115014	+	0.199211i	−0.802771	+	0.596287i	$0.796642\pi$
$138$	−49093.7	+	85032.8i	−0.219446	+	0.380092i
$139$	−223787.			−0.982422			−0.491211	−	0.871041i	$-0.663446\pi$
$139$	−223787.			−0.982422			−0.491211	+	0.871041i	$0.663446\pi$
$140$		0			0
$141$	−66666.6			−0.282397
$142$	120460.	−	208644.i	0.501330	−	0.868329i
$143$	4965.84	+	8601.09i	0.0203073	+	0.0351733i
$144$	−10368.0	−	17957.9i	−0.0416667	−	0.0721688i
$145$	13193.5	−	22851.8i	0.0521122	−	0.0902610i
$146$	307834.			1.19518
$147$		0			0
$148$	48615.9			0.182442
$149$	−129761.	+	224752.i	−0.478825	+	0.829350i	−0.999705	−	0.0242802i	$-0.992271\pi$
$149$	−129761.	+	224752.i	−0.478825	+	0.829350i	0.520880	+	0.853630i	$0.325604\pi$
$150$	55885.1	+	96795.8i	0.202800	+	0.351260i
$151$	55446.4	+	96036.0i	0.197893	+	0.342761i	0.947845	−	0.318731i	$-0.103257\pi$
$151$	55446.4	+	96036.0i	0.197893	+	0.342761i	−0.749952	+	0.661492i	$0.769923\pi$
$152$	−20332.1	+	35216.2i	−0.0713793	+	0.123633i
$153$	−2694.56			−0.00930592
$154$		0			0
$155$	1256.82			0.00420188
$156$	6154.36	−	10659.7i	0.0202475	−	0.0350697i
$157$	−202693.	−	351074.i	−0.656280	−	1.13671i	−0.981571	−	0.191096i	$-0.938796\pi$
$157$	−202693.	−	351074.i	−0.656280	−	1.13671i	0.325291	−	0.945614i	$-0.394538\pi$
$158$	−67192.0	−	116380.i	−0.214129	−	0.370882i
$159$	−61644.6	+	106772.i	−0.193376	+	0.334937i
$160$	4610.59			0.0142382
$161$		0			0
$162$	−26244.0			−0.0785674
$163$	−19309.3	+	33444.8i	−0.0569244	+	0.0985959i	−0.893083	−	0.449891i	$-0.851463\pi$
$163$	−19309.3	+	33444.8i	−0.0569244	+	0.0985959i	0.836159	+	0.548487i	$0.184796\pi$
$164$	6555.32	+	11354.1i	0.0190320	+	0.0329644i
$165$	2354.19	+	4077.57i	0.00673180	+	0.0116598i
$166$	−121150.	+	209838.i	−0.341234	+	0.591035i
$167$	207255.			0.575060			0.287530	−	0.957772i	$-0.407166\pi$
$167$	207255.			0.575060			0.287530	+	0.957772i	$0.407166\pi$
$168$		0			0
$169$	−363987.			−0.980322
$170$	299.563	−	518.859i	0.000794999	−	0.00137698i
$171$	25732.8	+	44570.4i	0.0672971	+	0.116562i
$172$	−88801.7	−	153809.i	−0.228876	−	0.396425i
$173$	−64128.7	+	111074.i	−0.162906	+	0.282161i	−0.935910	−	0.352240i	$-0.885420\pi$
$173$	−64128.7	+	111074.i	−0.162906	+	0.282161i	0.773004	+	0.634401i	$0.218753\pi$
$174$	210977.			0.528278
$175$		0			0
$176$	−29744.9			−0.0723820
$177$	−100691.	+	174401.i	−0.241577	+	0.418424i
$178$	−184380.	−	319356.i	−0.436179	−	0.755483i
$179$	49299.7	+	85389.6i	0.115004	+	0.199192i	0.917781	−	0.397086i	$-0.129979\pi$
$179$	49299.7	+	85389.6i	0.115004	+	0.199192i	−0.802778	+	0.596279i	$0.796645\pi$
$180$	2917.64	−	5053.49i	0.00671197	−	0.0116255i
$181$	−599225.			−1.35954			−0.679772	−	0.733423i	$-0.737921\pi$
$181$	−599225.			−1.35954			−0.679772	+	0.733423i	$0.737921\pi$
$182$		0			0
$183$	−114229.			−0.252144
$184$	87277.7	−	151169.i	0.190046	−	0.329169i
$185$	6840.44	+	11848.0i	0.0146945	+	0.0254516i
$186$	5024.45	+	8702.61i	0.0106489	+	0.0184445i
$187$	−1932.61	+	3347.38i	−0.00404148	+	0.00700005i
$188$	118518.			0.244563
$189$		0			0
$190$	−11443.2			−0.0229966
$191$	−414608.	+	718122.i	−0.822346	+	1.42434i	0.0815852	+	0.996666i	$0.474002\pi$
$191$	−414608.	+	718122.i	−0.822346	+	1.42434i	−0.903931	+	0.427678i	$0.859332\pi$
$192$	18432.0	+	31925.2i	0.0360844	+	0.0625000i
$193$	208193.	+	360600.i	0.402320	+	0.696839i	0.994006	−	0.109330i	$-0.0348705\pi$
$193$	208193.	+	360600.i	0.402320	+	0.696839i	−0.591685	+	0.806169i	$0.701537\pi$
$194$	−304574.	+	527537.i	−0.581016	+	1.00635i
$195$	3463.77			0.00652323
$196$		0			0
$197$	−592061.			−1.08693			−0.543464	−	0.839433i	$-0.682887\pi$
$197$	−592061.			−1.08693			−0.543464	+	0.839433i	$0.682887\pi$
$198$	−18822.9	+	32602.3i	−0.0341212	+	0.0590996i
$199$	−533040.	−	923253.i	−0.954173	−	1.65268i	−0.736249	−	0.676711i	$-0.763405\pi$
$199$	−533040.	−	923253.i	−0.954173	−	1.65268i	−0.217925	−	0.975966i	$-0.569929\pi$
$200$	−99351.3	−	172081.i	−0.175630	−	0.304200i
$201$	−235365.	+	407664.i	−0.410915	+	0.711725i
$202$	430577.			0.742458
$203$		0			0
$204$	4790.33			0.00805916
$205$	−1844.72	+	3195.14i	−0.00306581	+	0.00531014i
$206$	−241278.	−	417906.i	−0.396142	−	0.686137i
$207$	−110461.	−	191324.i	−0.179177	−	0.310344i
$208$	−10941.1	+	18950.5i	−0.0175349	+	0.0303713i
$209$	73825.0			0.116906
$210$		0			0
$211$	−846029.			−1.30822			−0.654108	−	0.756401i	$-0.726956\pi$
$211$	−846029.			−1.30822			−0.654108	+	0.756401i	$0.726956\pi$
$212$	109590.	−	189816.i	0.167468	−	0.290064i
$213$	271036.	+	469448.i	0.409334	+	0.708988i
$214$	172229.	+	298309.i	0.257082	+	0.445278i
$215$	24989.5	−	43283.1i	0.0368690	−	0.0638590i
$216$	46656.0			0.0680414
$217$		0			0
$218$	264557.			0.377032
$219$	−346313.	+	599831.i	−0.487931	+	0.845121i
$220$	−4185.22	−	7249.01i	−0.00582991	−	0.0100977i
$221$	1421.75	+	2462.54i	0.00195814	+	0.00339159i
$222$	−54692.8	+	94730.8i	−0.0744814	+	0.129006i
$223$	−112299.			−0.151222			−0.0756109	−	0.997137i	$-0.524091\pi$
$223$	−112299.			−0.151222			−0.0756109	+	0.997137i	$0.524091\pi$
$224$		0			0
$225$	−251483.			−0.331171
$226$	263217.	−	455904.i	0.342801	−	0.593749i
$227$	−89238.4	−	154565.i	−0.114944	−	0.199089i	0.802813	−	0.596231i	$-0.203336\pi$
$227$	−89238.4	−	154565.i	−0.114944	−	0.199089i	−0.917757	+	0.397141i	$0.870002\pi$
$228$	−45747.1	−	79236.3i	−0.0582810	−	0.100946i
$229$	229877.	−	398158.i	0.289672	−	0.501726i	−0.684060	−	0.729426i	$-0.739787\pi$
$229$	229877.	−	398158.i	0.289672	−	0.501726i	0.973731	+	0.227700i	$0.0731205\pi$
$230$	49121.2			0.0612280
$231$		0			0
$232$	−375071.			−0.457502
$233$	−374334.	+	648365.i	−0.451720	+	0.782402i	−0.998493	−	0.0548792i	$-0.982523\pi$
$233$	−374334.	+	648365.i	−0.451720	+	0.782402i	0.546773	+	0.837281i	$0.315856\pi$
$234$	13847.3	+	23984.3i	0.0165320	+	0.0286343i
$235$	16676.0	+	28883.7i	0.0196980	+	0.0341179i
$236$	179006.	−	310047.i	0.209212	−	0.362366i
$237$	302364.			0.349670
$238$		0			0
$239$	−814752.			−0.922637			−0.461319	−	0.887235i	$-0.652623\pi$
$239$	−814752.			−0.922637			−0.461319	+	0.887235i	$0.652623\pi$
$240$	−5186.91	+	8983.99i	−0.00581274	+	0.0100680i
$241$	−523816.	−	907276.i	−0.580947	−	1.00623i	−0.995367	−	0.0961439i	$-0.969349\pi$
$241$	−523816.	−	907276.i	−0.580947	−	1.00623i	0.414421	−	0.910085i	$-0.363984\pi$
$242$	−295101.	−	511131.i	−0.323916	−	0.561039i
$243$	29524.5	−	51137.9i	0.0320750	−	0.0555556i
$244$	203073.			0.218363
$245$		0			0
$246$	−29498.9			−0.0310791
$247$	27155.1	−	47034.1i	0.0283211	−	0.0490535i
$248$	−8932.36	−	15471.3i	−0.00922226	−	0.0159734i
$249$	−272587.	−	472135.i	−0.278617	−	0.482578i
$250$	56099.0	−	97166.3i	0.0567682	−	0.0983254i
$251$	1.09401e6			1.09607			0.548034	−	0.836456i	$-0.315377\pi$
$251$	1.09401e6			1.09607			0.548034	+	0.836456i	$0.315377\pi$
$252$		0			0
$253$	−316902.			−0.311261
$254$	28874.5	−	50012.2i	0.0280822	−	0.0486398i
$255$	674.018	+	1167.43i	0.000649114	+	0.00112430i
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	−389195.	+	674106.i	−0.367566	+	0.636642i	−0.989184	−	0.146678i	$-0.953142\pi$
$257$	−389195.	+	674106.i	−0.367566	+	0.636642i	0.621619	+	0.783320i	$0.286475\pi$
$258$	399608.			0.373753
$259$		0			0
$260$	−6157.82			−0.00564928
$261$	−237350.	+	411101.i	−0.215669	+	0.373549i
$262$	−638433.	−	1.10580e6i	−0.574595	−	0.995228i
$263$	−554881.	−	961083.i	−0.494664	−	0.856784i	0.505317	−	0.862934i	$-0.331376\pi$
$263$	−554881.	−	961083.i	−0.494664	−	0.856784i	−0.999981	+	0.00615004i	$0.998042\pi$
$264$	33463.0	−	57959.6i	0.0295498	−	0.0511818i
$265$	61679.2			0.0539540
$266$		0			0
$267$	829711.			0.712277
$268$	418427.	−	724736.i	0.355863	−	0.616372i
$269$	668202.	+	1.15736e6i	0.563024	+	0.975187i	0.997230	+	0.0743731i	$0.0236956\pi$
$269$	668202.	+	1.15736e6i	0.563024	+	0.975187i	−0.434206	+	0.900813i	$0.642971\pi$
$270$	6564.68	+	11370.4i	0.00548030	+	0.00949216i
$271$	896005.	−	1.55193e6i	0.741118	−	1.28365i	−0.210869	−	0.977514i	$-0.567629\pi$
$271$	896005.	−	1.55193e6i	0.741118	−	1.28365i	0.951987	−	0.306140i	$-0.0990374\pi$
$272$	−8516.14			−0.00697944
$273$		0			0
$274$	202136.			0.162655
$275$	−180371.	+	312411.i	−0.143825	+	0.249112i
$276$	196375.	+	340131.i	0.155172	+	0.268766i
$277$	−28788.8	−	49863.6i	−0.0225436	−	0.0390467i	0.854533	−	0.519396i	$-0.173843\pi$
$277$	−28788.8	−	49863.6i	−0.0225436	−	0.0390467i	−0.877077	+	0.480350i	$0.840510\pi$
$278$	−447574.	+	775221.i	−0.347339	+	0.601608i
$279$	−22610.0			−0.0173897
$280$		0			0
$281$	−550257.			−0.415719			−0.207860	−	0.978159i	$-0.566650\pi$
$281$	−550257.			−0.415719			−0.207860	+	0.978159i	$0.566650\pi$
$282$	−133333.	+	230940.i	−0.0998425	+	0.172932i
$283$	−588940.	−	1.02007e6i	−0.437125	−	0.757122i	0.560342	−	0.828261i	$-0.310670\pi$
$283$	−588940.	−	1.02007e6i	−0.437125	−	0.757122i	−0.997466	+	0.0711395i	$0.977336\pi$
$284$	−481842.	−	834575.i	−0.354494	−	0.614001i
$285$	12873.6	−	22297.7i	0.00938832	−	0.0162610i
$286$	39726.7			0.0287189
$287$		0			0
$288$	−82944.0			−0.0589256
$289$	709375.	−	1.22867e6i	0.499610	−	0.865350i
$290$	−52773.9	−	91407.1i	−0.0368489	−	0.0638242i
$291$	−685290.	−	1.18696e6i	−0.474397	−	0.821680i
$292$	615667.	−	1.06637e6i	0.422560	−	0.731896i
$293$	−300762.			−0.204670			−0.102335	−	0.994750i	$-0.532631\pi$
$293$	−300762.			−0.204670			−0.102335	+	0.994750i	$0.532631\pi$
$294$		0			0
$295$	100747.			0.0674028
$296$	97231.7	−	168410.i	0.0645028	−	0.111722i
$297$	−42351.6	−	73355.1i	−0.0278598	−	0.0482547i
$298$	519042.	+	899008.i	0.338581	+	0.586439i
$299$	−116567.	+	201899.i	−0.0754043	+	0.130604i
$300$	447081.			0.286802
$301$		0			0
$302$	443571.			0.279863
$303$	−484399.	+	839003.i	−0.303107	+	0.524997i
$304$	81328.2	+	140865.i	0.0504728	+	0.0874214i
$305$	28573.2	+	49490.3i	0.0175877	+	0.0304628i
$306$	−5389.12	+	9334.23i	−0.00329014	+	0.00569869i
$307$	−146787.			−0.0888874			−0.0444437	−	0.999012i	$-0.514152\pi$
$307$	−146787.			−0.0888874			−0.0444437	+	0.999012i	$0.514152\pi$
$308$		0			0
$309$	1.08575e6			0.646896
$310$	2513.64	−	4353.75i	0.00148559	−	0.00257311i
$311$	851554.	+	1.47494e6i	0.499242	+	0.864713i	1.00000		0.000874814i	$-0.000278462\pi$
$311$	851554.	+	1.47494e6i	0.499242	+	0.864713i	−0.500757	+	0.865588i	$0.666945\pi$
$312$	−24617.5	−	42638.7i	−0.0143172	−	0.0247980i
$313$	558474.	−	967305.i	0.322212	−	0.558088i	−0.658732	−	0.752378i	$-0.728907\pi$
$313$	558474.	−	967305.i	0.322212	−	0.558088i	0.980944	+	0.194290i	$0.0622403\pi$
$314$	−1.62154e6			−0.928120
$315$		0			0
$316$	−537536.			−0.302824
$317$	481447.	−	833891.i	0.269092	−	0.466081i	−0.699536	−	0.714598i	$-0.746610\pi$
$317$	481447.	−	833891.i	0.269092	−	0.466081i	0.968628	+	0.248517i	$0.0799432\pi$
$318$	246578.	+	427086.i	0.136737	+	0.236836i
$319$	340467.	+	589707.i	0.187326	+	0.324459i
$320$	9221.17	−	15971.5i	0.00503398	−	0.00871910i
$321$	−775029.			−0.419812
$322$		0			0
$323$	21136.5			0.0112727
$324$	−52488.0	+	90911.9i	−0.0277778	+	0.0481125i
$325$	132692.	+	229829.i	0.0696844	+	0.120697i
$326$	77237.3	+	133779.i	0.0402516	+	0.0697178i
$327$	−297626.	+	515504.i	−0.153922	+	0.266602i
$328$	52442.5			0.0269153
$329$		0			0
$330$	18833.5			0.00952020
$331$	1.12998e6	−	1.95718e6i	0.566891	−	0.981883i	−0.429980	−	0.902838i	$-0.641480\pi$
$331$	1.12998e6	−	1.95718e6i	0.566891	−	0.981883i	0.996871	−	0.0790451i	$-0.0251871\pi$
$332$	484600.	+	839351.i	0.241289	+	0.417925i
$333$	−123059.	−	213144.i	−0.0608138	−	0.105333i
$334$	414509.	−	717951.i	0.203314	−	0.352151i
$335$	235497.			0.114650
$336$		0			0
$337$	1.33338e6			0.639557			0.319778	−	0.947492i	$-0.396392\pi$
$337$	1.33338e6			0.639557			0.319778	+	0.947492i	$0.396392\pi$
$338$	−727973.	+	1.26089e6i	−0.346596	+	0.600322i
$339$	592237.	+	1.02578e6i	0.279896	+	0.484794i
$340$	−1198.25	−	2075.44i	−0.000562149	−	0.000973671i
$341$	−16216.6	+	28087.9i	−0.00755219	+	0.0130808i
$342$	205862.			0.0951724
$343$		0			0
$344$	−710414.			−0.323680
$345$	−55261.4	+	95715.5i	−0.0249962	+	0.0432947i
$346$	256515.	+	444296.i	0.115192	+	0.199518i
$347$	717431.	+	1.24263e6i	0.319857	+	0.554009i	0.980458	−	0.196728i	$-0.0630317\pi$
$347$	717431.	+	1.24263e6i	0.319857	+	0.554009i	−0.660601	+	0.750737i	$0.729698\pi$
$348$	421955.	−	730847.i	0.186775	−	0.323503i
$349$	−3.34711e6			−1.47098			−0.735489	−	0.677536i	$-0.763048\pi$
$349$	−3.34711e6			−1.47098			−0.735489	+	0.677536i	$0.763048\pi$
$350$		0			0
$351$	−62312.9			−0.0269967
$352$	−59489.7	+	103039.i	−0.0255909	+	0.0443247i
$353$	2.00209e6	+	3.46772e6i	0.855160	+	1.48118i	0.876497	+	0.481408i	$0.159874\pi$
$353$	2.00209e6	+	3.46772e6i	0.855160	+	1.48118i	−0.0213370	+	0.999772i	$0.506792\pi$
$354$	402763.	+	697605.i	0.170821	+	0.295870i
$355$	135594.	−	234856.i	0.0571044	−	0.0989078i
$356$	−1.47504e6			−0.616850
$357$		0			0
$358$	394398.			0.162640
$359$	297993.	−	516139.i	0.122031	−	0.211364i	−0.798538	−	0.601945i	$-0.794393\pi$
$359$	297993.	−	516139.i	0.122031	−	0.211364i	0.920568	+	0.390581i	$0.127726\pi$
$360$	−11670.5	−	20214.0i	−0.00474608	−	0.00822045i
$361$	1.03620e6	+	1.79475e6i	0.418480	+	0.724828i
$362$	−1.19845e6	+	2.07578e6i	−0.480672	+	0.832548i
$363$	1.32796e6			0.528953
$364$		0			0
$365$	346507.			0.136138
$366$	−228458.	+	395700.i	−0.0891462	+	0.154406i
$367$	−1.65195e6	−	2.86126e6i	−0.640224	−	1.10890i	−0.985383	−	0.170356i	$-0.945508\pi$
$367$	−1.65195e6	−	2.86126e6i	−0.640224	−	1.10890i	0.345159	−	0.938544i	$-0.387825\pi$
$368$	−349111.	−	604677.i	−0.134383	−	0.232758i
$369$	33186.3	−	57480.3i	0.0126880	−	0.0219762i
$370$	54723.5			0.0207812
$371$		0			0
$372$	40195.6			0.0150599
$373$	1.41532e6	−	2.45140e6i	0.526722	−	0.912309i	−0.472794	−	0.881173i	$-0.656754\pi$
$373$	1.41532e6	−	2.45140e6i	0.526722	−	0.912309i	0.999515	−	0.0311353i	$-0.00991229\pi$
$374$	7730.45	+	13389.5i	0.00285776	+	0.00494979i
$375$	126223.	+	218624.i	0.0463510	+	0.0802824i
$376$	237037.	−	410560.i	0.0864661	−	0.149764i
$377$	500938.			0.181523
$378$		0			0
$379$	2.45025e6			0.876218			0.438109	−	0.898922i	$-0.355648\pi$
$379$	2.45025e6			0.876218			0.438109	+	0.898922i	$0.355648\pi$
$380$	−22886.4	+	39640.4i	−0.00813052	+	0.0140825i
$381$	64967.7	+	112527.i	0.0229290	+	0.0397142i
$382$	1.65843e6	+	2.87249e6i	0.581486	+	1.00716i
$383$	−1.69202e6	+	2.93067e6i	−0.589399	+	1.02087i	0.404912	+	0.914356i	$0.367302\pi$
$383$	−1.69202e6	+	2.93067e6i	−0.589399	+	1.02087i	−0.994311	+	0.106514i	$0.966031\pi$
$384$	147456.			0.0510310
$385$		0			0
$386$	1.66554e6			0.568967
$387$	−449559.	+	778659.i	−0.152584	+	0.264283i
$388$	1.21829e6	+	2.11015e6i	0.410840	+	0.711596i
$389$	2.07480e6	+	3.59366e6i	0.695189	+	1.20410i	0.970117	+	0.242638i	$0.0780127\pi$
$389$	2.07480e6	+	3.59366e6i	0.695189	+	1.20410i	−0.274928	+	0.961465i	$0.588654\pi$
$390$	6927.54	−	11998.9i	0.00230631	−	0.00399465i
$391$	−90731.0			−0.0300133
$392$		0			0
$393$	2.87295e6			0.938310
$394$	−1.18412e6	+	2.05096e6i	−0.384287	+	0.665605i
$395$	−75633.4	−	131001.i	−0.0243905	−	0.0422456i
$396$	75291.7	+	130409.i	0.0241273	+	0.0417898i
$397$	−823330.	+	1.42605e6i	−0.262179	+	0.454107i	−0.966821	−	0.255456i	$-0.917774\pi$
$397$	−823330.	+	1.42605e6i	−0.262179	+	0.454107i	0.704642	+	0.709563i	$0.251108\pi$
$398$	−4.26432e6			−1.34940
$399$		0			0
$400$	−794810.			−0.248378
$401$	2.19332e6	−	3.79894e6i	0.681147	−	1.17978i	−0.293484	−	0.955964i	$-0.594815\pi$
$401$	2.19332e6	−	3.79894e6i	0.681147	−	1.17978i	0.974631	−	0.223817i	$-0.0718520\pi$
$402$	941460.	+	1.63066e6i	0.290561	+	0.503266i
$403$	11929.9	+	20663.2i	0.00365910	+	0.00633775i
$404$	861153.	−	1.49156e6i	0.262499	−	0.454661i
$405$	−29541.1			−0.00894929
$406$		0			0
$407$	−353045.			−0.105644
$408$	9580.65	−	16594.2i	0.00284934	−	0.00493521i
$409$	177296.	+	307086.i	0.0524072	+	0.0907719i	0.891039	−	0.453927i	$-0.149977\pi$
$409$	177296.	+	307086.i	0.0524072	+	0.0907719i	−0.838632	+	0.544699i	$0.816644\pi$
$410$	7378.87	+	12780.6i	0.00216786	+	0.00375484i
$411$	−227403.	+	393873.i	−0.0664035	+	0.115014i
$412$	−1.93023e6			−0.560229
$413$		0			0
$414$	−883686.			−0.253395
$415$	−136370.	+	236200.i	−0.0388686	+	0.0673224i
$416$	43764.4	+	75802.1i	0.0123990	+	0.0214757i
$417$	−1.00704e6	−	1.74425e6i	−0.283601	−	0.491211i
$418$	147650.	−	255737.i	0.0413326	−	0.0715902i
$419$	1.79802e6			0.500335			0.250167	−	0.968203i	$-0.419514\pi$
$419$	1.79802e6			0.500335			0.250167	+	0.968203i	$0.419514\pi$
$420$		0			0
$421$	6.10881e6			1.67978			0.839888	−	0.542760i	$-0.182621\pi$
$421$	6.10881e6			1.67978			0.839888	+	0.542760i	$0.182621\pi$
$422$	−1.69206e6	+	2.93073e6i	−0.462524	+	0.801115i
$423$	−300000.	−	519615.i	−0.0815211	−	0.141199i
$424$	−438362.	−	759265.i	−0.118418	−	0.205106i
$425$	−51641.2	+	89445.1i	−0.0138683	+	0.0240206i
$426$	2.16829e6			0.578886
$427$		0			0
$428$	1.37783e6			0.363568
$429$	−44692.6	+	77409.8i	−0.0117244	+	0.0203073i
$430$	−99958.0	−	173132.i	−0.0260703	−	0.0451551i
$431$	955880.	+	1.65563e6i	0.247862	+	0.429310i	0.962932	−	0.269743i	$-0.0869387\pi$
$431$	955880.	+	1.65563e6i	0.247862	+	0.429310i	−0.715070	+	0.699053i	$0.753605\pi$
$432$	93312.0	−	161621.i	0.0240563	−	0.0416667i
$433$	−385530.			−0.0988186			−0.0494093	−	0.998779i	$-0.515734\pi$
$433$	−385530.			−0.0988186			−0.0494093	+	0.998779i	$0.515734\pi$
$434$		0			0
$435$	237483.			0.0601740
$436$	529114.	−	916452.i	0.133301	−	0.230884i
$437$	866472.	+	1.50077e6i	0.217046	+	0.375934i
$438$	1.38525e6	+	2.39933e6i	0.345019	+	0.597591i
$439$	−916909.	+	1.58813e6i	−0.227073	+	0.393302i	−0.956939	−	0.290288i	$-0.906249\pi$
$439$	−916909.	+	1.58813e6i	−0.227073	+	0.393302i	0.729866	+	0.683590i	$0.239582\pi$
$440$	−33481.8			−0.00824473
$441$		0			0
$442$	11374.0			0.00276922
$443$	966960.	−	1.67482e6i	0.234099	−	0.405471i	−0.724912	−	0.688842i	$-0.758119\pi$
$443$	966960.	−	1.67482e6i	0.234099	−	0.405471i	0.959010	+	0.283371i	$0.0914527\pi$
$444$	218771.	+	378923.i	0.0526663	+	0.0912208i
$445$	−207544.	−	359477.i	−0.0496833	−	0.0860540i
$446$	−224598.	+	389016.i	−0.0534650	+	0.0926041i
$447$	−2.33569e6			−0.552900
$448$		0			0
$449$	6.76354e6			1.58328			0.791641	−	0.610987i	$-0.209227\pi$
$449$	6.76354e6			1.58328			0.791641	+	0.610987i	$0.209227\pi$
$450$	−502966.	+	871162.i	−0.117087	+	0.202800i
$451$	−47604.3	−	82453.0i	−0.0110206	−	0.0190882i
$452$	−1.05287e6	−	1.82362e6i	−0.242397	−	0.419844i
$453$	−499018.	+	864324.i	−0.114254	+	0.197893i
$454$	−713907.			−0.162556
$455$		0			0
$456$	−365977.			−0.0824217
$457$	1.19746e6	−	2.07406e6i	0.268207	−	0.464548i	−0.700192	−	0.713955i	$-0.746902\pi$
$457$	1.19746e6	−	2.07406e6i	0.268207	−	0.464548i	0.968399	+	0.249407i	$0.0802356\pi$
$458$	−919507.	−	1.59263e6i	−0.204829	−	0.354774i
$459$	−12125.5	−	21002.0i	−0.00268639	−	0.00465296i
$460$	98242.5	−	170161.i	0.0216474	−	0.0374943i
$461$	6.42949e6			1.40904			0.704522	−	0.709682i	$-0.251162\pi$
$461$	6.42949e6			1.40904			0.704522	+	0.709682i	$0.251162\pi$
$462$		0			0
$463$	1.36524e6			0.295976			0.147988	−	0.988989i	$-0.452720\pi$
$463$	1.36524e6			0.295976			0.147988	+	0.988989i	$0.452720\pi$
$464$	−750142.	+	1.29928e6i	−0.161752	+	0.280162i
$465$	5655.68	+	9795.93i	0.00121298	+	0.00210094i
$466$	1.49733e6	+	2.59346e6i	0.319414	+	0.553241i
$467$	2.18181e6	−	3.77900e6i	0.462940	−	0.801835i	−0.536166	−	0.844113i	$-0.680128\pi$
$467$	2.18181e6	−	3.77900e6i	0.462940	−	0.801835i	0.999106	+	0.0422772i	$0.0134613\pi$
$468$	110779.			0.0233798
$469$		0			0
$470$	133408.			0.0278572
$471$	1.82423e6	−	3.15967e6i	0.378903	−	0.656280i
$472$	−716022.	−	1.24019e6i	−0.147935	−	0.256231i
$473$	644872.	+	1.11695e6i	0.132532	+	0.229552i
$474$	604728.	−	1.04742e6i	0.123627	−	0.214129i
$475$	1.97267e6			0.401163
$476$		0			0
$477$	−1.10960e6			−0.223291
$478$	−1.62950e6	+	2.82239e6i	−0.326201	+	0.564998i
$479$	−696248.	−	1.20594e6i	−0.138652	−	0.240152i	0.788335	−	0.615247i	$-0.210944\pi$
$479$	−696248.	−	1.20594e6i	−0.138652	−	0.240152i	−0.926986	+	0.375095i	$0.877610\pi$
$480$	20747.6	+	35936.0i	0.00411022	+	0.00711912i
$481$	−129861.	+	224926.i	−0.0255927	+	0.0443278i
$482$	−4.19053e6			−0.821583
$483$		0			0
$484$	−2.36081e6			−0.458087
$485$	−342837.	+	593812.i	−0.0661811	+	0.114629i
$486$	−118098.	−	204552.i	−0.0226805	−	0.0392837i
$487$	−4.91460e6	−	8.51233e6i	−0.939000	−	1.62640i	−0.767341	−	0.641239i	$-0.778421\pi$
$487$	−4.91460e6	−	8.51233e6i	−0.939000	−	1.62640i	−0.171659	−	0.985156i	$-0.554913\pi$
$488$	406147.	−	703467.i	0.0772029	−	0.133719i
$489$	−347568.			−0.0657306
$490$		0			0
$491$	−7.67255e6			−1.43627			−0.718135	−	0.695904i	$-0.755004\pi$
$491$	−7.67255e6			−1.43627			−0.718135	+	0.695904i	$0.755004\pi$
$492$	−58997.9	+	102187.i	−0.0109881	+	0.0190320i
$493$	97477.9	+	168837.i	0.0180630	+	0.0312859i
$494$	−108621.	−	188136.i	−0.0200260	−	0.0346861i
$495$	−21187.7	+	36698.1i	−0.00388660	+	0.00673180i
$496$	−71458.9			−0.0130422
$497$		0			0
$498$	−2.18070e6			−0.394024
$499$	−1.69691e6	+	2.93914e6i	−0.305076	+	0.528408i	−0.977278	−	0.211960i	$-0.932015\pi$
$499$	−1.69691e6	+	2.93914e6i	−0.305076	+	0.528408i	0.672202	+	0.740368i	$0.265349\pi$
$500$	−224396.	−	388665.i	−0.0401412	−	0.0695266i
$501$	932646.	+	1.61539e6i	0.166006	+	0.287530i
$502$	2.18802e6	−	3.78976e6i	0.387518	−	0.671201i
$503$	8.36268e6			1.47376			0.736878	−	0.676026i	$-0.236299\pi$
$503$	8.36268e6			1.47376			0.736878	+	0.676026i	$0.236299\pi$
$504$		0			0
$505$	484671.			0.0845704
$506$	−633805.	+	1.09778e6i	−0.110047	+	0.190607i
$507$	−1.63794e6	−	2.83700e6i	−0.282995	−	0.490161i
$508$	−115498.	−	200049.i	−0.0198571	−	0.0343935i
$509$	1.93662e6	−	3.35432e6i	0.331322	−	0.573866i	−0.651450	−	0.758692i	$-0.725839\pi$
$509$	1.93662e6	−	3.35432e6i	0.331322	−	0.573866i	0.982771	+	0.184826i	$0.0591722\pi$
$510$	5392.14			0.000917986
$511$		0			0
$512$	−262144.			−0.0441942
$513$	−231595.	+	401134.i	−0.0388540	+	0.0672971i
$514$	1.55678e6	+	2.69642e6i	0.259908	+	0.450174i
$515$	−271590.	−	470409.i	−0.0451228	−	0.0781551i
$516$	799216.	−	1.38428e6i	0.132142	−	0.228876i
$517$	−860672.			−0.141616
$518$		0			0
$519$	−1.15432e6			−0.188108
$520$	−12315.6	+	21331.3i	−0.00199732	+	0.00345947i
$521$	365532.	+	633120.i	0.0589971	+	0.102186i	0.894015	−	0.448036i	$-0.147876\pi$
$521$	365532.	+	633120.i	0.0589971	+	0.102186i	−0.835018	+	0.550222i	$0.814543\pi$
$522$	949398.	+	1.64441e6i	0.152501	+	0.264139i
$523$	−3.55427e6	+	6.15618e6i	−0.568193	+	0.984140i	0.428551	+	0.903517i	$0.359024\pi$
$523$	−3.55427e6	+	6.15618e6i	−0.568193	+	0.984140i	−0.996745	+	0.0806223i	$0.974309\pi$
$524$	−5.10746e6			−0.812600
$525$		0			0
$526$	−4.43905e6			−0.699561
$527$	−4642.90	+	8041.73i	−0.000728220	+	0.00126131i
$528$	−133852.	−	231838.i	−0.0208949	−	0.0361910i
$529$	−501258.	−	868205.i	−0.0778794	−	0.134891i
$530$	123358.	−	213663.i	0.0190756	−	0.0330400i
$531$	−1.81243e6			−0.278949
$532$		0			0
$533$	−70041.3			−0.0106791
$534$	1.65942e6	−	2.87420e6i	0.251828	−	0.436179i
$535$	193866.	+	335786.i	0.0292831	+	0.0507198i
$536$	−1.67371e6	−	2.89895e6i	−0.251633	−	0.435841i
$537$	−443698.	+	768507.i	−0.0663974	+	0.115004i
$538$	5.34562e6			0.796237
$539$		0			0
$540$	52517.5			0.00775031
$541$	−1.89757e6	+	3.28669e6i	−0.278743	+	0.482798i	−0.971073	−	0.238784i	$-0.923251\pi$
$541$	−1.89757e6	+	3.28669e6i	−0.278743	+	0.482798i	0.692329	+	0.721582i	$0.256585\pi$
$542$	−3.58402e6	−	6.20771e6i	−0.524050	−	0.907680i
$543$	−2.69651e6	−	4.67050e6i	−0.392467	−	0.679772i
$544$	−17032.3	+	29500.8i	−0.00246760	+	0.00427401i
$545$	297793.			0.0429461
$546$		0			0
$547$	−1.34686e7			−1.92466			−0.962332	−	0.271879i	$-0.912355\pi$
$547$	−1.34686e7			−1.92466			−0.962332	+	0.271879i	$0.912355\pi$
$548$	404272.	−	700219.i	0.0575072	−	0.0996053i
$549$	−514030.	−	890325.i	−0.0727876	−	0.126072i
$550$	721482.	+	1.24964e6i	0.101700	+	0.176149i
$551$	1.86181e6	−	3.22474e6i	0.261250	−	0.452498i
$552$	1.57100e6			0.219446
$553$		0			0
$554$	−230310.			−0.0318815
$555$	−61564.0	+	106632.i	−0.00848387	+	0.0146945i
$556$	1.79030e6	+	3.10089e6i	0.245606	+	0.425401i
$557$	−2.44744e6	−	4.23908e6i	−0.334251	−	0.578941i	0.649089	−	0.760712i	$-0.275150\pi$
$557$	−2.44744e6	−	4.23908e6i	−0.334251	−	0.578941i	−0.983341	+	0.181772i	$0.941817\pi$
$558$	−45220.1	+	78323.5i	−0.00614817	+	0.0106489i
$559$	948816.			0.128426
$560$		0			0
$561$	−34787.0			−0.00466670
$562$	−1.10051e6	+	1.90615e6i	−0.146979	+	0.254575i
$563$	−3.12803e6	−	5.41790e6i	−0.415910	−	0.720378i	0.579613	−	0.814892i	$-0.303204\pi$
$563$	−3.12803e6	−	5.41790e6i	−0.415910	−	0.720378i	−0.995524	+	0.0945139i	$0.969870\pi$
$564$	533333.	+	923759.i	0.0705993	+	0.122282i
$565$	296285.	−	513180.i	0.0390470	−	0.0676315i
$566$	−4.71152e6			−0.618188
$567$		0			0
$568$	−3.85474e6			−0.501330
$569$	−714125.	+	1.23690e6i	−0.0924685	+	0.160160i	−0.908549	−	0.417778i	$-0.862809\pi$
$569$	−714125.	+	1.23690e6i	−0.0924685	+	0.160160i	0.816081	+	0.577938i	$0.196142\pi$
$570$	−51494.4	−	89190.9i	−0.00663854	−	0.0114983i
$571$	−4.52573e6	−	7.83880e6i	−0.580897	−	1.00614i	−0.995373	−	0.0960825i	$-0.969369\pi$
$571$	−4.52573e6	−	7.83880e6i	−0.580897	−	1.00614i	0.414477	−	0.910060i	$-0.363965\pi$
$572$	79453.5	−	137617.i	0.0101537	−	0.0175867i
$573$	−7.46295e6			−0.949563
$574$		0			0
$575$	−8.46792e6			−1.06809
$576$	−165888.	+	287326.i	−0.0208333	+	0.0360844i
$577$	4.00960e6	+	6.94482e6i	0.501373	+	0.868404i	0.999999	+	0.00158626i	$0.000504922\pi$
$577$	4.00960e6	+	6.94482e6i	0.501373	+	0.868404i	−0.498626	+	0.866817i	$0.666162\pi$
$578$	−2.83750e6	−	4.91470e6i	−0.353278	−	0.611895i
$579$	−1.87373e6	+	3.24540e6i	−0.232280	+	0.402320i
$580$	−422191.			−0.0521122
$581$		0			0
$582$	−5.48232e6			−0.670899
$583$	−795838.	+	1.37843e6i	−0.0969735	+	0.167963i
$584$	−2.46267e6	−	4.26547e6i	−0.298795	−	0.517529i
$585$	15587.0	+	26997.4i	0.00188309	+	0.00326162i
$586$	−601524.	+	1.04187e6i	−0.0723617	+	0.125334i
$587$	8.28470e6			0.992388			0.496194	−	0.868212i	$-0.334730\pi$
$587$	8.28470e6			0.992388			0.496194	+	0.868212i	$0.334730\pi$
$588$		0			0
$589$	177357.			0.0210649
$590$	201494.	−	348998.i	0.0238305	−	0.0412756i
$591$	−2.66427e6	−	4.61466e6i	−0.313769	−	0.543464i
$592$	−388927.	−	673641.i	−0.0456104	−	0.0789995i
$593$	2.95722e6	−	5.12205e6i	0.345340	−	0.598146i	−0.640076	−	0.768312i	$-0.721097\pi$
$593$	2.95722e6	−	5.12205e6i	0.345340	−	0.598146i	0.985415	+	0.170166i	$0.0544304\pi$
$594$	−338813.			−0.0393998
$595$		0			0
$596$	4.15234e6			0.478825
$597$	4.79736e6	−	8.30927e6i	0.550892	−	0.954173i
$598$	466266.	+	807597.i	0.0533189	+	0.0923510i
$599$	−1.66449e6	−	2.88298e6i	−0.189545	−	0.328302i	0.755553	−	0.655087i	$-0.227368\pi$
$599$	−1.66449e6	−	2.88298e6i	−0.189545	−	0.328302i	−0.945099	+	0.326785i	$0.894035\pi$
$600$	894161.	−	1.54873e6i	0.101400	−	0.175630i
$601$	4.87081e6			0.550066			0.275033	−	0.961435i	$-0.411311\pi$
$601$	4.87081e6			0.550066			0.275033	+	0.961435i	$0.411311\pi$
$602$		0			0
$603$	−4.23657e6			−0.474484
$604$	887142.	−	1.53658e6i	0.0989466	−	0.171381i
$605$	−332175.	−	575345.i	−0.0368960	−	0.0639057i
$606$	1.93760e6	+	3.35601e6i	0.214329	+	0.371229i
$607$	−7.58504e6	+	1.31377e7i	−0.835577	+	1.44726i	0.0579835	+	0.998318i	$0.481533\pi$
$607$	−7.58504e6	+	1.31377e7i	−0.835577	+	1.44726i	−0.893560	+	0.448944i	$0.851800\pi$
$608$	650626.			0.0713793
$609$		0			0
$610$	228586.			0.0248728
$611$	−316582.	+	548336.i	−0.0343070	+	0.0594216i
$612$	21556.5	+	37336.9i	0.00232648	+	0.00402958i
$613$	−2.59078e6	−	4.48736e6i	−0.278471	−	0.482325i	0.692534	−	0.721385i	$-0.256494\pi$
$613$	−2.59078e6	−	4.48736e6i	−0.278471	−	0.482325i	−0.971005	+	0.239060i	$0.923161\pi$
$614$	−293573.	+	508483.i	−0.0314264	+	0.0544322i
$615$	−33204.9			−0.00354009
$616$		0			0
$617$	1.55854e6			0.164818			0.0824092	−	0.996599i	$-0.473739\pi$
$617$	1.55854e6			0.164818			0.0824092	+	0.996599i	$0.473739\pi$
$618$	2.17151e6	−	3.76116e6i	0.228712	−	0.396142i
$619$	−703756.	−	1.21894e6i	−0.0738236	−	0.127866i	0.826750	−	0.562569i	$-0.190187\pi$
$619$	−703756.	−	1.21894e6i	−0.0738236	−	0.127866i	−0.900574	+	0.434703i	$0.856854\pi$
$620$	−10054.5	−	17415.0i	−0.00105047	−	0.00181947i
$621$	994147.	−	1.72191e6i	0.103448	−	0.179177i
$622$	6.81243e6			0.706035
$623$		0			0
$624$	−196940.			−0.0202475
$625$	−4.78799e6	+	8.29304e6i	−0.490290	+	0.849207i
$626$	−2.23389e6	−	3.86922e6i	−0.227838	−	0.394628i
$627$	332213.	+	575409.i	0.0337479	+	0.0584531i
$628$	−3.24308e6	+	5.61719e6i	−0.328140	+	0.568355i
$629$	−101079.			−0.0101867
$630$		0			0
$631$	−1.09643e7			−1.09624			−0.548120	−	0.836399i	$-0.684656\pi$
$631$	−1.09643e7			−1.09624			−0.548120	+	0.836399i	$0.684656\pi$
$632$	−1.07507e6	+	1.86208e6i	−0.107064	+	0.185441i
$633$	−3.80713e6	−	6.59415e6i	−0.377649	−	0.654108i
$634$	−1.92579e6	−	3.33556e6i	−0.190277	−	0.329569i
$635$	32502.1	−	56295.3i	0.00319873	−	0.00554036i
$636$	1.97263e6			0.193376
$637$		0			0
$638$	2.72374e6			0.264919
$639$	−2.43932e6	+	4.22503e6i	−0.236329	+	0.409334i
$640$	−36884.7	−	63886.2i	−0.00355956	−	0.00616534i
$641$	7.10609e6	+	1.23081e7i	0.683103	+	1.18317i	0.974029	+	0.226423i	$0.0727032\pi$
$641$	7.10609e6	+	1.23081e7i	0.683103	+	1.18317i	−0.290926	+	0.956745i	$0.593964\pi$
$642$	−1.55006e6	+	2.68478e6i	−0.148426	+	0.257082i
$643$	9.13928e6			0.871735			0.435868	−	0.900011i	$-0.356442\pi$
$643$	9.13928e6			0.871735			0.435868	+	0.900011i	$0.356442\pi$
$644$		0			0
$645$	449811.			0.0425727
$646$	42273.1	−	73219.1i	0.00398550	−	0.00690309i
$647$	−9.46362e6	−	1.63915e7i	−0.888785	−	1.53942i	−0.841313	−	0.540549i	$-0.818217\pi$
$647$	−9.46362e6	−	1.63915e7i	−0.888785	−	1.53942i	−0.0474724	−	0.998873i	$-0.515117\pi$
$648$	209952.	+	363648.i	0.0196419	+	0.0340207i
$649$	−1.29993e6	+	2.25154e6i	−0.121145	+	0.209830i
$650$	1.06153e6			0.0985487
$651$		0			0
$652$	617899.			0.0569244
$653$	2.14991e6	−	3.72376e6i	0.197305	−	0.341742i	−0.750349	−	0.661042i	$-0.770114\pi$
$653$	2.14991e6	−	3.72376e6i	0.197305	−	0.341742i	0.947654	+	0.319300i	$0.103448\pi$
$654$	1.19051e6	+	2.06202e6i	0.108840	+	0.188516i
$655$	−718640.	−	1.24472e6i	−0.0654498	−	0.113362i
$656$	104885.	−	181666.i	0.00951599	−	0.0164822i
$657$	−6.23363e6			−0.563414
$658$		0			0
$659$	−1.15303e7			−1.03425			−0.517126	−	0.855909i	$-0.672998\pi$
$659$	−1.15303e7			−1.03425			−0.517126	+	0.855909i	$0.672998\pi$
$660$	37667.0	−	65241.1i	0.00336590	−	0.00582991i
$661$	7.35237e6	+	1.27347e7i	0.654521	+	1.13366i	0.982014	+	0.188810i	$0.0604631\pi$
$661$	7.35237e6	+	1.27347e7i	0.654521	+	1.13366i	−0.327492	+	0.944854i	$0.606204\pi$
$662$	−4.51990e6	−	7.82870e6i	−0.400852	−	0.694296i
$663$	−12795.8	+	22162.9i	−0.00113053	+	0.00195814i
$664$	3.87680e6			0.341234
$665$		0			0
$666$	−984471.			−0.0860037
$667$	−7.99202e6	+	1.38426e7i	−0.695572	+	1.20477i
$668$	−1.65804e6	−	2.87181e6i	−0.143765	−	0.249008i
$669$	−505346.	−	875286.i	−0.0436540	−	0.0756109i
$670$	470994.	−	815786.i	0.0405349	−	0.0702084i
$671$	−1.47471e6			−0.126444
$672$		0			0
$673$	1.42971e7			1.21678			0.608389	−	0.793639i	$-0.291816\pi$
$673$	1.42971e7			1.21678			0.608389	+	0.793639i	$0.291816\pi$
$674$	2.66676e6	−	4.61896e6i	0.226117	−	0.391647i
$675$	−1.13167e6	−	1.96012e6i	−0.0956008	−	0.165585i
$676$	2.91189e6	+	5.04355e6i	0.245080	+	0.424492i
$677$	4.56012e6	−	7.89836e6i	0.382389	−	0.662316i	−0.609015	−	0.793159i	$-0.708435\pi$
$677$	4.56012e6	−	7.89836e6i	0.382389	−	0.662316i	0.991403	+	0.130843i	$0.0417683\pi$
$678$	4.73790e6			0.395832
$679$		0			0
$680$	−9586.03			−0.000794999
$681$	803146.	−	1.39109e6i	0.0663631	−	0.114944i
$682$	64866.2	+	112352.i	0.00534020	+	0.00924950i
$683$	7.25762e6	+	1.25706e7i	0.595309	+	1.03111i	0.993503	+	0.113804i	$0.0363037\pi$
$683$	7.25762e6	+	1.25706e7i	0.595309	+	1.03111i	−0.398194	+	0.917301i	$0.630363\pi$
$684$	411724.	−	713127.i	0.0336485	−	0.0582810i
$685$	227530.			0.0185273
$686$		0			0
$687$	4.13778e6			0.334484
$688$	−1.42083e6	+	2.46095e6i	−0.114438	+	0.198212i
$689$	585468.	+	1.01406e6i	0.0469846	+	0.0813796i
$690$	221046.	+	382862.i	0.0176750	+	0.0306140i
$691$	1.04254e6	−	1.80573e6i	0.0830608	−	0.143866i	−0.821502	−	0.570205i	$-0.806864\pi$
$691$	1.04254e6	−	1.80573e6i	0.0830608	−	0.143866i	0.904563	+	0.426339i	$0.140197\pi$
$692$	2.05212e6			0.162906
$693$		0			0
$694$	5.73945e6			0.452347
$695$	−503804.	+	872613.i	−0.0395639	+	0.0685267i
$696$	−1.68782e6	−	2.92339e6i	−0.132070	−	0.228751i
$697$	−13629.4	−	23606.8i	−0.00106266	−	0.00184058i
$698$	−6.69422e6	+	1.15947e7i	−0.520069	+	0.900787i
$699$	−6.73801e6			−0.521601
$700$		0			0
$701$	9.96513e6			0.765928			0.382964	−	0.923763i	$-0.374903\pi$
$701$	9.96513e6			0.765928			0.382964	+	0.923763i	$0.374903\pi$
$702$	−124626.	+	215858.i	−0.00954477	+	0.0165320i
$703$	965293.	+	1.67194e6i	0.0736667	+	0.127594i
$704$	237959.	+	412157.i	0.0180955	+	0.0313423i
$705$	−150084.	+	259953.i	−0.0113726	+	0.0196980i
$706$	1.60167e7			1.20938
$707$		0			0
$708$	3.22210e6			0.241577
$709$	−3.54518e6	+	6.14043e6i	−0.264864	+	0.458757i	−0.967528	−	0.252764i	$-0.918660\pi$
$709$	−3.54518e6	+	6.14043e6i	−0.264864	+	0.458757i	0.702664	+	0.711522i	$0.251994\pi$
$710$	−542376.	−	939423.i	−0.0403789	−	0.0699384i
$711$	1.36064e6	+	2.35669e6i	0.100941	+	0.174835i
$712$	−2.95008e6	+	5.10969e6i	−0.218089	+	0.377742i
$713$	−761324.			−0.0560849
$714$		0			0
$715$	44717.6			0.00327125
$716$	788796.	−	1.36623e6i	0.0575019	−	0.0995962i
$717$	−3.66639e6	−	6.35037e6i	−0.266342	−	0.461319i
$718$	−1.19197e6	−	2.06456e6i	−0.0862889	−	0.149457i
$719$	6.00833e6	−	1.04067e7i	0.433443	−	0.750745i	−0.563724	−	0.825963i	$-0.690632\pi$
$719$	6.00833e6	−	1.04067e7i	0.433443	−	0.750745i	0.997167	+	0.0752181i	$0.0239653\pi$
$720$	−93364.4			−0.00671197
$721$		0			0
$722$	8.28958e6			0.591820
$723$	4.71435e6	−	8.16549e6i	0.335410	−	0.580947i
$724$	4.79380e6	+	8.30310e6i	0.339886	+	0.588700i
$725$	9.09760e6	+	1.57575e7i	0.642809	+	1.11338i
$726$	2.65591e6	−	4.60017e6i	0.187013	−	0.323916i
$727$	−1.32577e7			−0.930318			−0.465159	−	0.885227i	$-0.654003\pi$
$727$	−1.32577e7			−0.930318			−0.465159	+	0.885227i	$0.654003\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$	693014.	−	1.20034e6i	0.0481321	−	0.0833673i
$731$	184631.	+	319790.i	0.0127794	+	0.0221346i
$732$	913830.	+	1.58280e6i	0.0630359	+	0.109181i
$733$	−454651.	+	787479.i	−0.0312549	+	0.0541351i	−0.881230	−	0.472688i	$-0.843284\pi$
$733$	−454651.	+	787479.i	−0.0312549	+	0.0541351i	0.849975	+	0.526823i	$0.176617\pi$
$734$	−1.32156e7			−0.905413
$735$		0			0
$736$	−2.79289e6			−0.190046
$737$	−3.03859e6	+	5.26299e6i	−0.206064	+	0.356914i
$738$	−132745.	−	229921.i	−0.00897176	−	0.0155396i
$739$	143426.	+	248421.i	0.00966086	+	0.0167331i	0.870815	−	0.491610i	$-0.163591\pi$
$739$	143426.	+	248421.i	0.00966086	+	0.0167331i	−0.861155	+	0.508343i	$0.830258\pi$
$740$	109447.	−	189568.i	0.00734725	−	0.0127258i
$741$	488792.			0.0327024
$742$		0			0
$743$	−1.35906e6			−0.0903163			−0.0451582	−	0.998980i	$-0.514379\pi$
$743$	−1.35906e6			−0.0903163			−0.0451582	+	0.998980i	$0.514379\pi$
$744$	80391.3	−	139242.i	0.00532447	−	0.00922226i
$745$	584250.	+	1.01195e6i	0.0385663	+	0.0667988i
$746$	−5.66126e6	−	9.80559e6i	−0.372448	−	0.645100i
$747$	2.45329e6	−	4.24921e6i	0.160859	−	0.278617i
$748$	61843.6			0.00404148
$749$		0			0
$750$	1.00978e6			0.0655503
$751$	−7.72018e6	+	1.33718e7i	−0.499491	+	0.865144i	−1.00000		0.000587430i	$-0.999813\pi$
$751$	−7.72018e6	+	1.33718e7i	−0.499491	+	0.865144i	0.500509	+	0.865732i	$0.333146\pi$
$752$	−948147.	−	1.64224e6i	−0.0611408	−	0.105899i
$753$	4.92305e6	+	8.52697e6i	0.316407	+	0.548034i
$754$	1.00188e6	−	1.73530e6i	0.0641779	−	0.111159i
$755$	499298.			0.0318781
$756$		0			0
$757$	1.70683e7			1.08256			0.541279	−	0.840843i	$-0.317940\pi$
$757$	1.70683e7			1.08256			0.541279	+	0.840843i	$0.317940\pi$
$758$	4.90050e6	−	8.48792e6i	0.309790	−	0.536572i
$759$	−1.42606e6	−	2.47001e6i	−0.0898532	−	0.155630i
$760$	91545.6	+	158562.i	0.00574915	+	0.00995782i
$761$	1.54173e6	−	2.67035e6i	0.0965041	−	0.167150i	−0.813731	−	0.581241i	$-0.802567\pi$
$761$	1.54173e6	−	2.67035e6i	0.0965041	−	0.167150i	0.910235	+	0.414091i	$0.135901\pi$
$762$	519742.			0.0324265
$763$		0			0
$764$	1.32675e7			0.822346
$765$	−6066.16	+	10506.9i	−0.000374766	+	0.000649114i
$766$	6.76810e6	+	1.17227e7i	0.416768	+	0.721864i
$767$	956307.	+	1.65637e6i	0.0586960	+	0.101665i
$768$	294912.	−	510803.i	0.0180422	−	0.0312500i
$769$	−3.00821e7			−1.83439			−0.917195	−	0.398439i	$-0.869552\pi$
$769$	−3.00821e7			−1.83439			−0.917195	+	0.398439i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	294.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 - 3.46410i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(2.25126 - 3.89930i) q^{5} +36.0000 q^{6} -64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(q+(2.00000 - 3.46410i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(2.25126 - 3.89930i) q^{5} +36.0000 q^{6} -64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-9.00505 - 15.5972i) q^{10} +(58.0955 + 100.624i) q^{11} +(72.0000 - 124.708i) q^{12} +85.4773 q^{13} +40.5227 q^{15} +(-128.000 + 221.703i) q^{16} +(16.6331 + 28.8093i) q^{17} +(162.000 + 280.592i) q^{18} +(317.688 - 550.252i) q^{19} -72.0404 q^{20} +464.764 q^{22} +(-1363.71 + 2362.02i) q^{23} +(-288.000 - 498.831i) q^{24} +(1552.36 + 2688.77i) q^{25} +(170.955 - 296.102i) q^{26} -729.000 q^{27} +5860.48 q^{29} +(81.0455 - 140.375i) q^{30} +(139.568 + 241.739i) q^{31} +(512.000 + 886.810i) q^{32} +(-522.859 + 905.619i) q^{33} +133.065 q^{34} +1296.00 q^{36} +(-1519.25 + 2631.41i) q^{37} +(-1270.75 - 2201.01i) q^{38} +(384.648 + 666.229i) q^{39} +(-144.081 + 249.555i) q^{40} -819.415 q^{41} +11100.2 q^{43} +(929.527 - 1609.99i) q^{44} +(182.352 + 315.843i) q^{45} +(5454.85 + 9448.09i) q^{46} +(-3703.70 + 6415.00i) q^{47} -2304.00 q^{48} +12418.9 q^{50} +(-149.698 + 259.284i) q^{51} +(-683.818 - 1184.41i) q^{52} +(6849.40 + 11863.5i) q^{53} +(-1458.00 + 2525.33i) q^{54} +523.153 q^{55} +5718.39 q^{57} +(11721.0 - 20301.3i) q^{58} +(11187.8 + 19377.9i) q^{59} +(-324.182 - 561.499i) q^{60} +(-6346.04 + 10991.7i) q^{61} +1116.55 q^{62} +4096.00 q^{64} +(192.432 - 333.302i) q^{65} +(2091.44 + 3622.47i) q^{66} +(26151.7 + 45296.0i) q^{67} +(266.129 - 460.949i) q^{68} -24546.8 q^{69} +60230.2 q^{71} +(2592.00 - 4489.48i) q^{72} +(38479.2 + 66647.9i) q^{73} +(6076.98 + 10525.6i) q^{74} +(-13971.3 + 24199.0i) q^{75} -10166.0 q^{76} +3077.18 q^{78} +(16798.0 - 29095.0i) q^{79} +(576.323 + 998.221i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(-1638.83 + 2838.54i) q^{82} -60574.9 q^{83} +149.782 q^{85} +(22200.4 - 38452.3i) q^{86} +(26372.2 + 45677.9i) q^{87} +(-3718.11 - 6439.95i) q^{88} +(46095.1 - 79839.0i) q^{89} +1458.82 q^{90} +43638.8 q^{92} +(-1256.11 + 2175.65i) q^{93} +(14814.8 + 25660.0i) q^{94} +(-1430.40 - 2477.53i) q^{95} +(-4608.00 + 7981.29i) q^{96} -152287. q^{97} -9411.46 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} + 18 q^{3} - 32 q^{4} + 108 q^{5} + 144 q^{6} - 256 q^{8} - 162 q^{9}+O(q^{10}) \) 4 * q + 8 * q^2 + 18 * q^3 - 32 * q^4 + 108 * q^5 + 144 * q^6 - 256 * q^8 - 162 * q^9	\( 4 q + 8 q^{2} + 18 q^{3} - 32 q^{4} + 108 q^{5} + 144 q^{6} - 256 q^{8} - 162 q^{9} - 432 q^{10} - 124 q^{11} + 288 q^{12} - 1440 q^{13} + 1944 q^{15} - 512 q^{16} - 1260 q^{17} + 648 q^{18} + 360 q^{19} - 3456 q^{20} - 992 q^{22} - 6524 q^{23} - 1152 q^{24} - 4482 q^{25} - 2880 q^{26} - 2916 q^{27} + 14176 q^{29} + 3888 q^{30} + 5904 q^{31} + 2048 q^{32} + 1116 q^{33} - 10080 q^{34} + 5184 q^{36} + 6040 q^{37} - 1440 q^{38} - 6480 q^{39} - 6912 q^{40} + 34776 q^{41} - 1216 q^{43} - 1984 q^{44} + 8748 q^{45} + 26096 q^{46} - 30456 q^{47} - 9216 q^{48} - 35856 q^{50} + 11340 q^{51} + 11520 q^{52} - 3964 q^{53} - 5832 q^{54} - 48672 q^{55} + 6480 q^{57} + 28352 q^{58} + 40752 q^{59} - 15552 q^{60} - 1368 q^{61} + 47232 q^{62} + 16384 q^{64} - 82980 q^{65} - 4464 q^{66} + 16224 q^{67} - 20160 q^{68} - 117432 q^{69} - 6408 q^{71} + 10368 q^{72} + 23976 q^{73} - 24160 q^{74} + 40338 q^{75} - 11520 q^{76} - 51840 q^{78} + 82160 q^{79} + 27648 q^{80} - 13122 q^{81} + 69552 q^{82} - 347472 q^{83} - 267400 q^{85} - 2432 q^{86} + 63792 q^{87} + 7936 q^{88} + 200556 q^{89} + 69984 q^{90} + 208768 q^{92} - 53136 q^{93} + 121824 q^{94} + 25640 q^{95} - 18432 q^{96} - 503856 q^{97} + 20088 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 + 18 * q^3 - 32 * q^4 + 108 * q^5 + 144 * q^6 - 256 * q^8 - 162 * q^9 - 432 * q^10 - 124 * q^11 + 288 * q^12 - 1440 * q^13 + 1944 * q^15 - 512 * q^16 - 1260 * q^17 + 648 * q^18 + 360 * q^19 - 3456 * q^20 - 992 * q^22 - 6524 * q^23 - 1152 * q^24 - 4482 * q^25 - 2880 * q^26 - 2916 * q^27 + 14176 * q^29 + 3888 * q^30 + 5904 * q^31 + 2048 * q^32 + 1116 * q^33 - 10080 * q^34 + 5184 * q^36 + 6040 * q^37 - 1440 * q^38 - 6480 * q^39 - 6912 * q^40 + 34776 * q^41 - 1216 * q^43 - 1984 * q^44 + 8748 * q^45 + 26096 * q^46 - 30456 * q^47 - 9216 * q^48 - 35856 * q^50 + 11340 * q^51 + 11520 * q^52 - 3964 * q^53 - 5832 * q^54 - 48672 * q^55 + 6480 * q^57 + 28352 * q^58 + 40752 * q^59 - 15552 * q^60 - 1368 * q^61 + 47232 * q^62 + 16384 * q^64 - 82980 * q^65 - 4464 * q^66 + 16224 * q^67 - 20160 * q^68 - 117432 * q^69 - 6408 * q^71 + 10368 * q^72 + 23976 * q^73 - 24160 * q^74 + 40338 * q^75 - 11520 * q^76 - 51840 * q^78 + 82160 * q^79 + 27648 * q^80 - 13122 * q^81 + 69552 * q^82 - 347472 * q^83 - 267400 * q^85 - 2432 * q^86 + 63792 * q^87 + 7936 * q^88 + 200556 * q^89 + 69984 * q^90 + 208768 * q^92 - 53136 * q^93 + 121824 * q^94 + 25640 * q^95 - 18432 * q^96 - 503856 * q^97 + 20088 * q^99

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